Answers
The equivalent of the expression 2³/2⁷ using the law of indices is (a) 1/2⁴
How to determine the equivalent expression?From the question, we have the following parameters that can be used in our computation:
2³/2⁷
The above expression can be solved using the law of indices
When the law of indices is applied, we have the following representation
2³/2⁷ = 2(³ ⁻ ⁷)
Remove the bracket in the above expression
So, we have the following representation
2³/2⁷ = 2³ ⁻ ⁷
Evaluate the difference
This gives
2³/2⁷ = 2⁻⁴
Rewrite as
2³/2⁷ = 1/2⁴
Hence, the solution is (a) 1/2⁴
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Related Questions
If the volume of a cone is 30pi³ and the radius is 5 cm, what is the height?
Answers
Answer:
h≈1.15cm is the correct answer
Answer: h is about 1.15 cm
Step-by-step explanation:
The CEO of a company wants to determine if taking the employees to a company retreat would boost their morale. He decides to use a random number table to survey a simple random sample of 50 of the 250 employees. Which of the following correctly labels the population of employees?
A. 000–250
B. 001–250
C. 0–250
D. 1–250
Answers
The correctly labels the population of employees is, 001 - 250.
What is population?
The term "population" refers to all citizens who are either permanently residing in a nation or are only temporarily absent from it. This indicator displays the population of a given area on a regular basis. Growth rates are the yearly changes in population brought on by births, deaths, and net migration.
Given:
The CEO of a company wants to determine if taking the employees to a company retreat would boost their morale.
He decides to use a random number table to survey a simple random sample of 50 of the 250 employees.
As the population consist of 250 employees and simple random sample of size 50, to use a random number table to survey a sample random sample of 50 of the 250 employees, the population of employees should be labeled as 001-250.
Hence, the correctly labels the population of employees is, 001 - 250.
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a farm has 22 cows and chicken altogether. Each cow has four legs, and each chicken has two legs. The farmer counted 62 legs total. How many cows are on the farm? How many chickens?
Answers
The number of cows are 9 and the number of chickens are 13.
Given that, a farm has 22 cows and chicken altogether.
What is a linear system of equations?A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.
Let the x be the number of cows and y be the number of chicken.
Now, x+y=22 -------(I)
The farmer counted 62 legs total.
So, 4x+2y=62 -------(II)
Multiply equation (I) by 2, we get
2x+2y=44 -------(III)
Subtract equation (III) from equation (II), we get
4x+2y-(2x+2y)=62-44
⇒ 2x=18
⇒ x=9
Substitute x=9 in equation (I), we get
9+y=22
⇒ y=13
Hence, the number of cows are 9 and the number of chickens are 13.
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help meeeeeeeeeee pleaseee
Answers
For an average intake of 2200 calories per day, the number of acres of land is approximately 2.
How to solve function?A function having the formula f(x) = ax' + b is said to be linear.
It appears to be a standard linear equation, except the linear function symbol is f rather than y. (x).
You would be given the value of f(x) and asked to locate x when solving a linear function.
C(x) is a variable that tells the number of calories consumed daily by a person
x is the number of acres that person own.
C(x) = 270ln(x+1)+1900
In the given question number of acres ask a person have who consumed 2200 calories in a day.
Therefore,
C(x)=2200
2200=270ln(x+1)+1900
2200-1900=270ln(x+1)
300=270ln(x+1)
300/270 = ㏑(x+1)
10/9 = ㏑(x+1)
x+1 = e^(10/9)
x+1 = 3.037
x= 3.037-1
x=2.037
x=2(round off)
Therefore, 2 acres of land a person can consume 2200 calories in a day.
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Sketch the curve with the given vector equation. Indicate with an arrow the direction in which t increases.
Answers
Refer to the attachment for graph.
What are vector equations ?
Vector equations allow for the creation of parametric curves. That is, points in space are formed for each value of the parameter by the equation of a vector, where each of its elements has a function with an independent variable that we refer to as a parameter.
Given vector equation:
r(t) = < t², t, 2 >
When t= -2,
r(-2) = < (-2)², -2, 2 >
= < 4, -2, 2 >
This means. when t= -2, the curve touches the point ( 4, -2, 2 )
Similarly, when t= -1, the curve touches the point ( 1, -1, 2 )
Table is attached.
graph is attached.
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URGENT!! ILL GIVE BRAINLIEST!!!! AND 100 POINTS!!!
Answers
Answer: False
Step-by-step explanation:
(TONS OF POINTS AND BRAINLYEST GURANTEE) Please answer the question that is stated in the image below. Thank you. It really means a lot to me.
Answers
Answer:
Below
Step-by-step explanation:
a) All possible rolls ( 36 of them)
1 1 , 2 , 3 , 4 , 5 , 6
2 1, 2, 3, 4, 5 , 6
3 1 , 2 , 3 , 4,5,6
4 1,2,3,4,5,6
5 1,2,3,4,5,6
6 1,2,3,4,5,6
b) underlined above 21 out of 36 or 7/12
c ) 3 out of 36 1/12
d ) 11/36
Express in scientific notation and then solve.
There was a total of $9.48 million contributed to a political campaign by 79 thousand
people. What was the average contribution?
Answers
Answer:
the average contribution to the political campaign was $0.12.
Step-by-step explanation:
To find the average contribution to the political campaign, we first need to convert the total amount of money contributed and the number of people who contributed to scientific notation.
The total amount of money contributed to the political campaign was $9.48 million, which can be written in scientific notation as $9.48 * 10^6.
The number of people who contributed to the campaign was 79 thousand, which can be written in scientific notation as 79 * 10^3.
To find the average contribution, we need to divide the total amount of money contributed by the number of people who contributed. Therefore, we can substitute the values in scientific notation into the formula to find the average contribution:
Average contribution = Total amount / Number of people
= 9.48 * 10^6 / 79 * 10^3
= 9.48 / 79
= 0.12
Therefore, the average contribution to the political campaign was $0.12.
A postage box should weigh 1.0 punds. If there is a 5% error on the weight, what is the range of acceptable weight
Answers
Answer:
0.95-1.05 (please give brainliest)
Step-by-step explanation
1x.95=.95
1x1.05=1.05
Suppose that 11 inches of wire costs 33 cents. At the same rate, how much (in cents) will 5 inches of wire cost?
Answers
Answer:
15 cents
Step-by-step explanation:
[tex]\frac{11}{33} =\frac{5}{y}[/tex]
Cross Multiply.
11 · y = 5 · 33
11y = 165
11y ÷ 11 = 165 ÷ 11
y = 15
To raise funds for the local animal shelter, a group of BYU-Idaho students sold collars and scratching posts. The first week they sold seven collars and 10 scratching posts and donated $299.83. The second week they sold nine collars and 18 scratching posts and donated $482.85. "Because it is difficult to make two different items, they want to sell only one item during the last two weeks of the fundraiser. They decide to sell only the item for which they can donate the most money per item sold.
Answers
By using simultaneous linear equation, it can be concluded that-
They should sell only scratching post during the last two weeks of the fundraiser
Third option is correct
What is simultaneous linear equation?
At first, it is important to know about linear equation.
Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign
A one degree equation is known as linear equation.
Two or more linear equations, which can be solved together to obtain common solution are known as simultaneous linear equation.
Here, a system of simultaneous linear equation needs to be solved
Let the cost of one collar be $x and the cost of one scratching post be $y
The first week they sold seven collars and 10 scratching posts and donated $299.83.
7x + 10y = 299.83 ..... (1)
The second week they sold nine collars and 18 scratching posts and donated $482.85.
9x + 18y = 482.85 .... (2)
Multiplying (1) by 9 and (2) by 5
63x + 90y = 2698.47 ..... (3)
45x + 90y = 2414.25 ... (4)
Subraction (4) from (3)
18x = 284.22
x = [tex]\frac{284.22}{18}[/tex]
x = $15.79
Putting the value of x in (1)
7 [tex]\times[/tex] 15.79 + 10y = 299.83
110.53 + 10y = 299.83
10y = 299.83 - 110.53
10y = 189.3
y = [tex]\frac{189.3}{10}[/tex]
y = $18.93
Since the cost of one scratching post is more than cost of one collars, they should sold scratching post during the last two weeks of the fundrasiser
Third option is correct
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Complete Question
The complete Question has been attached
Pablo bought 13 pounds of flour for 8$ how many pounds of flour did he get per pound
Answers
The amount of flour he get in per dollar will be;
⇒ 1.625 dollars
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Pablo bought 13 pounds of flour for $8.
Now,
Since, Pablo bought 13 pounds of flour for $8
Hence, The amount of flour he get in per dollar = 13/8
= 1.625 pounds
Thus, The amount of flour he get in per dollar will be;
⇒ 1.625 dollars
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Graph the following features:
Y intercept =-2
Slope =-2/3
Answers
The ratio of of distance between two places A and B and B to C is 4:5. If the distance between A to C is 72 km, find the distance between A to B.
Answers
the whole distance containing all three points will be AC, and we know that AC = 72 km, now point B is between splitting the AC segment into AB and BC to a 4 : 5 ratio.
well, hell for that let's simply grab the total amount of 72 and split it up by dividing it by (4 + 5) and distribute accordingly.
[tex]A\stackrel{\text{\LARGE 4}}{\rule[0.35em]{10em}{0.25pt}} B\stackrel{\text{\LARGE 5}}{\rule[0.35em]{14em}{0.25pt}} C \\\\\\ \stackrel{AB}{4}~~ : ~~\stackrel{BC}{5} ~~ \implies ~~ \stackrel{AB}{4\cdot \frac{72}{4+5}}~~ : ~~\stackrel{BC}{5\cdot \frac{72}{4+5}} \\\\\\ \stackrel{AB}{4\cdot 8}~~ : ~~\stackrel{BC}{5\cdot 8} ~~ \implies ~~ \stackrel{AB}{\text{\LARGE 32}}~~ : ~~\stackrel{BC}{40}[/tex]
(8.08) Graph the first six terms of a sequence where a1 = 3 and d = −10. (2 points) Group of answer choices graphed sequence showing point 1, negative 10, point 2, negative 7, point 3, negative 4, point 4, negative 1, point 5, 2, and point 6, 5 graphed sequence showing point 1, negative 7, point 2, negative 4, point 3, negative 1, point 4, 2, point 5, 5, and point 6, 8 graphed sequence showing point 1, 3, point 2, negative 7, point 3, negative 17, point 4, negative 27, point 5, negative 37, and point 6, negative 47 graphed sequence showing point 1, negative 7, point 2, negative 17, point 3, negative 27, point 4, negative 37, point 5, negative 47, and point 6, negative 57
Answers
The first six terms of the given sequence are given as 3, -7, -17, -27, -37 and -47.
What is an arithmetic sequence?An arithmetic sequence is a kind of sequence of numbers where the difference of any two consecutive terms are the same.
This difference is known as the common difference of the sequence.
The given problem can be solved as follows,
The first term of the sequence is a₁ = 3
And, the common difference is d = -10.
Now, the first six terms can be written as,
a₁ = 3
a₂ = 3 - 10
= -7
a₃ = -7 - 10
= -17
a₄ = -17 - 10
= -27
a₅ = -27 - 10
= -37
a₆ = -37 - 10
= -47
They can be graphed on the number line as follows,
Hence, the first six terms are given as 3, -7, -17, -27, -37 and -47.
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3
If f (x) = √2-x and g(x) = x-1, then find the domain of h (x) = f(x) = g(x).
O A.
(-∞0, 1) U (-1,2]
O B.
(-∞0, 1) U (1,2]
O C.
(-∞0, 2) U (1,2]
O D.
(-∞, -1) U (1,2]
O E. (-∞0,-2) U (1,2]
Reset
Next
Answers
Answer: B. ( - ∞ , 1 ) U ( 1, 2]
Step-by-step explanation:
The equation of H(x) is [tex]\frac{\sqrt{2-x} }{x-1}[/tex]
For the bottom denominator, x-1 cannot equal zero
x-1=0
x=1
For the numerator, 2-x square root has to be greater or equal to zero.
[tex]2-x\geq 0[/tex]
[tex]x\leq 2[/tex]
so the domain is
( - ∞ , 1 ) U ( 1, 2]
21 =6/11 a +3
Pls hurry I need this like by tonight, btw 6/11 is a fractionnn
Answers
Answer: a=33
Step-by-step explanation:
Answer:
a=33
Step-by-step explanation:
1. Multiply both sides of the equation by 11
231=6a+33
2. Move 6a to the left side by subtracting
231-6a=33
3. Move 231 to the right side by subtracting
-6a=33-231
4. Find the difference
-6a=-198
5. Divide -6 on both sides to get "a" by itself
a=33
Write an inequality that describes the safe speeds to drive according to the sign.
Speed Limit 65
Minimum 45
Answers
X ≤ 65 and x ≥ 45
Magan went to the grocery store and purchased cans of soup and frozen dinners.
Each can of soup has 350 mg of sodium and each frozen dinner has 650 mg of
sodium. Magan purchased a total of 11 cans of soup and frozen dinners which
collectively contain 4750 mg of sodium. Determine the number of cans of soup
purchased and the number of frozen dinners purchased.
Answers
The number of cans of soup purchased and the number of frozen dinners purchased are 8 and 3 respectively.
What is a system of equations?A system having more than two equations is known as a system of equations.
Given that, the can of soup contains 350 mg of sodium and the frozen dinner contain 650 mg of sodium.
Let the numbers of cans of soups and frozen dinners purchased be s and f, then,
s + f = 11
s = 11-f (1)
The total sodium in all 11 cans is 4750 mg which can be expressed as:
350s + 650f = 4750
Substitute s = (11-f) into the above equation:
350(11 - f) + 650f = 4750
3850 - 350f + 650f = 4750
300f = 4750 -3850
300f = 900
f = 3
Substitute f = 3 into equation (1):
s = 11-3
s = 8
Hence, the number of cans of soup purchased and the number of frozen dinners purchased are 8 and 3 respectively.
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At noon, ship A is 170 km west of ship B. Ship A is sailing east at 35 km/h and ship B is sailing north at 30 km/h. How fast (in km/hr) is the distance between the ships changing at 4:00 p.m.? (Round your answer to three decimal places.)
Answers
The speed (in km/hr) of the ships changing at 4.00pm is 20.62km/hr
How to calculate speed in a journey?The given parameters are;
The distance between A and B = 170km=m
The distance between B and C is 30km=m
Time is 12.00 noon to 4.00 pm = 4 hours
From the given parameters,
m=170-35*4 = 170-140=30
The Distance (D)=√(30²+120²
D=30*√(1²+4²)
Simplifying to get
30√17
From the Pythagoras theorem,
D²=m²+n²
Applying differential calculus,
⇒2m(dm/dt)+2n(dn/dt)=2D(dD/dt)
Applying the figures from the question we have
2*30*(-35)+2*120*30=2*30√17*dD/dt
Simplify to get
120-35=√17dD/dt
This implies that dD/dt=85/√17
⇒5√17=20.6155281km/h
Therefore, the speed between the ships is ≅20.62km/hr
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Simplify roots of negative numbers -14
Answers
Step-by-step explanation:
since it's -14 then it will be√-14
√-14=√-2 multiplied is by √7
so that will be √-2√7
if the area of the trapezoid is 70 square unites what is the length CE
Answers
the height of 4.6 units when the trapezoid's area is 70 units and its first and second bases are
what is area?Area is a mathematical concept that expresses the size of a region on a planar or curved surface. A shape's "space enclosed within the perimeter or the boundary" is referred to as its area. Math formulas are used to determine the area of various forms.
given
area of the trapezoid is 70 units
and the 1st base = 20 units and 2nd base = 10 units
length CE ?
area of trapezoid = 1/2( b1 + b2)*h
70= 1/2 (20 + 10 )*h
70 = 1/2(30)*h
h = 4.6 units
the height of 4.6 units when the trapezoid's area is 70 units and its first and second bases are
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Simplify each expression. Then drag and drop the equivalent matching expression.
3a+b+13a
20b+11a-5b
20b-5b+2b
You will not use all of the expressions.
Answers
From the expression, when simplified, (1) 16a+b (2) 17b+11a (3) 17b.
How to simplify algebraic expressions?An algebraic expression is an expression built up from integer constants, variables, and the algebraic operations.
The given algebraic terms are
3a+b+13a
Collect the like terms
3a+13a+b
Add the like terms
16a+b
Therefore, 3a+b+13a matches 16a+b
20b+11a-3b
Collect like terms
20b-3b+11a
=17b+11a
Therefore, 20b+11a-3b matches 17b+11a
20b-5b+2b
All the terms are alike, therefore do the arithmetic operation
15b+2b
=17b
Therefore, 20b-5b+2b matches 17b
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Pretzelmania, Incorporated, issues 7%, 10-year bonds with a face amount of $70,000 for $70,000 on January 1, 2024. Interest is paid annually on December 31.
Answers
Cr Cash 4,900 which is Interest paid annually on December 31.
What is Compound interest?Compound interest is defined as interest paid on the original principal and the interest earned on the interest of the principal.
Pretzelmania, Inc., issues 7%, 10-year bonds with a face amount of $70,000 $70,000 on January 1, 2015. The market interest rate for bonds of similar risk and maturity is 7%. Interest is paid annually on December 31.
January 1, 2015, bonds issued at par value
Dr Cash 70,000
Cr Bonds payable 70,000
June 30, 2015, first coupon payment
Dr Interest expense of 4,900
Cr Cash 4,900
Thus, Cr Cash 4,900 which is Interest paid annually on December 31.
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Suppose the coefficient of determination is 0.81, and the sample slope is negative. Then the coefficient of correlation is: a) 0.85 b) -0.85 c) 0.91 d) -0.90
Answers
The coefficient of correlation is -0.90
The percentage of the dependent variable's variance that is predicted from the independent variable is known as the coefficient of determination or R squared method. It shows how much variety there is in the given data collection.
The range of the coefficient of determination, which is the square of the correlation(r), is 0 to 1.
The square of the correlation between the x and y variables is used to calculate the coefficient of determination in linear regression.
The dependent variable cannot be predicted from the independent variable if R2 is equal to 0.
The dependent variable can be accurately predicted from the independent variable if R2 is equal to 1.
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what goes in the question marks?
OPTIONS:
1. Corresponding angles
2. definition of parallel lines
3. substitution property of equality
4. reflexive angles
5. segment bisector
Answers
By using the properties of parallel lines, it can be inferred that -
Corrosponding angle goes in the place of first question mark and substitution property of equality goes in the place of second question mark.
What are parallel lines?
Two lines are said to be parallel if on extending them indefinitely, they will never intersect
Transversal is a line that intersects two or more parallel lines
For the first question mark
[tex]\angle ASR \cong \angle AVU[/tex] [Corrosponding angle]
For the second question mark
[tex]m\angle AVU = 90^{\circ}[/tex] [Substitution property of equality]
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Find equations of (a) the tangent plane and (b) the normal line to the given surface at the specific point.2(x-2)^2 + (y-1)^2 + (z-3)^2 = 10 at (3,3,5,)(a) x+y+z=11(b) x-3=y-3=z-5
Answers
For the given surface ;
(a) the equation of the tangent is x + y + z = 11 ,
(b) equation of normal is (x - 3) [tex]=[/tex] (y - 3) = (z - 5) .
In the question ,
it is given that ,
the equation of the surface is 2(x-2)² + (y-1)² + (z-3)² = 10 ,
we have to find the equation of the tangent at (3,3,5) .
the partial derivative fₓ = 4(x -2)
[tex]f_{y}[/tex] = 2(y-1) and [tex]f_{z}[/tex] = 2(z-3) .
the partial derivatives at (3,3,5) will be fₓ = 4(3 -2) = 4
[tex]f_{y}[/tex] = 2(3-1) = 4 and [tex]f_{z}[/tex] = 2(5-3) = 4 .
Part(a)
the equation of tangent at the point (3,3,5) is
fₓ(x - x₁) + [tex]f_{y}[/tex](y - y₁) + [tex]f_{z}[/tex](z - z₁) = 0 ,
Substituting the values form above ,
we get ,
4(x-3) + 4(y-3) + 4(z-5) = 0
4x - 12 + 4y - 12 + 4z - 20 = 0
after simplifying , we have 4x + 4y + 4z = 44 .
dividing both sides by 4 ,
we get ,
x [tex]+[/tex] y [tex]+[/tex] z [tex]=[/tex] 11 .
Part(b) ,
the equation of Normal is ;
(x-x₁)/fₓ = (y-y₁)/ [tex]f_{y}[/tex] = (z-z₁)/ [tex]f_{z}[/tex]
(x - 3)/4 = (y - 3)/4 = (z - 5)/4
(x - 3) [tex]=[/tex] (y - 3) [tex]=[/tex] (z - 5)
Therefore , the equation of tangent is x + y + z = 11 , and equation of normal is (x - 3) = (y - 3) = (z - 5) .
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The percentage of titanium in an alloy used in aerospace castings is measured in 51 randomly selected parts. The sample standard deviation is s = 0.37 and the probability plot support the assumption that the population is normally distributed. Construct a 95% two-sided confidence interval for ?.
Answers
A 95% two-sided confidence interval is 0.46 < a <0.31 .
The formula for confidence interval for population standard deviation is,
[tex]s\sqrt{\frac{n-1}{X^{2} _{1-a/2,n-1} } }[/tex] < a < [tex]s\sqrt{\frac{n-1}{X^{2} _{a/2,n-1} } }[/tex]
Given in question,
Significance level, a = 1 - 0.95
= 0.05
Sample size, n = 51
Sample standard deviation, s = 0.37
By using chi-square distribution table, we get
[tex]X^{2} _{1-a/2,n-1}[/tex] = [tex]X^{2} _{0.975,50}[/tex]
= 32.36
[tex]X^{2} _{a/2,n-1}[/tex] = [tex]X^{2} _{0.025,50}[/tex]
= 71.42
Confidence interval for population standard deviation is :
[tex]0.37\sqrt{\frac{50}{32.36} }[/tex] < a < [tex]0.37\sqrt{\frac{50}{71.42} }[/tex]
0.45992018426 < a < 0.30958278534
Hence, a 95% two-sided confidence interval is 0.46 < a <0.31 .
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A line has a slope of -3/5 through which two points could this line pass
Answers
Answer:
(5,-3), (10,-6)
Step-by-step explanation:
when - 10 is subtracted from x the result is 6
Answers
Answer:
(-10) - (-16) = 6
Step-by-step explanation: